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Gradient Functions.  New words: Differentiation, derivative  New notation:  New process: Differentiating a function  New knowledge: When and why to.

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Presentation on theme: "Gradient Functions.  New words: Differentiation, derivative  New notation:  New process: Differentiating a function  New knowledge: When and why to."— Presentation transcript:

1 Gradient Functions

2  New words: Differentiation, derivative  New notation:  New process: Differentiating a function  New knowledge: When and why to differentiate a function

3 Gradient of Equation of this line......

4 Gradient of a Curve?

5  Can you see any connection between the gradient of x 2 (shown by the tangents) and different x values.connection

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23 22x is the same as 2x 1 22x 1  times by power  2x 1 22x 1  take 1 from power  2x 0 = 2(1)=2 FFor ax the derivative is just a 33 is the same as 3(x 0 ) 33x 0  times by power  0x3x 0 wwell that’ll be 0 then. 1 minute

24  Just differentiate one term at a time.  E.g. y = 5x 3 – 2x 2 + 4x – 3  Try f(x) = 7x 3 + 6x 2 – 9x minute

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27  You have 32 problems to solve  You may work alone or in pairs – but your scores go towards the table total  1 point for each problem solved  Once checked crumple and toss – 1 or 2 points for getting it in the bin!  96 points on offer

28  Write the gradient formula for the following... 1) y = x 2 – x8) f(x) = 2 – 3x 2 2) y = 4x 2 9) f(x) = 4x 3 – 5x ) y = 3x 2 – 2x10) f(x) = 7x 3 – 6x + 4x 2 4) y = 2 – 3x11) f(x) = 2x 4 – 5x 2 + 3x 5) y = x – 2 – 2x 2 12) f(x) = 9 6) y = 2 + 4x – 3x 2 13) 9x 7 – 4x 5 + 3x 2 7) y = 3x – 114) 8x 3 – 5x 4 + 8x 2 + 3x


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